7
Results of a Search for Sub-GeV Dark Matter Using 2013 LUX Data D.S. Akerib, 1, 2, 3 S. Alsum, 4 H.M. Ara´ ujo, 5 X. Bai, 6 J. Balajthy, 7 P. Beltrame, 8 E.P. Bernard, 9 A. Bernstein, 10 T.P. Biesiadzinski, 1, 2, 3 E.M. Boulton, 9, 11, 12 B. Boxer, 13 P. Br´ as, 14 S. Burdin, 13 D. Byram, 15, 16 M.C. Carmona-Benitez, 17 C. Chan, 18 J.E. Cutter, 7 T.J.R. Davison, 8 E. Druszkiewicz, 19 S.R. Fallon, 20 A. Fan, 2, 3 S. Fiorucci, 11, 18 R.J. Gaitskell, 18 J. Genovesi, 20 C. Ghag, 21 M.G.D. Gilchriese, 11 C. Gwilliam, 13 C.R. Hall, 22 S.J. Haselschwardt, 23 S.A. Hertel, 24, 11 D.P. Hogan, 9 M. Horn, 16, 9 D.Q. Huang, 18 C.M. Ignarra, 2, 3 R.G. Jacobsen, 9 O. Jahangir, 21 W. Ji, 1, 2, 3 K. Kamdin, 9, 11 K. Kazkaz, 10 D. Khaitan, 19 R. Knoche, 22 E.V. Korolkova, 25 S. Kravitz, 11 V.A. Kudryavtsev, 25 B.G. Lenardo, 7, 10 K.T. Lesko, 11 J. Liao, 18 J. Lin, 9 A. Lindote, 14 M.I. Lopes, 14 A. Manalaysay, 7 R.L. Mannino, 26, 4 N. Marangou, 5 M.F. Marzioni, 8 D.N. McKinsey, 9, 11 D.-M. Mei, 15 M. Moongweluwan, 19 J.A. Morad, 7 A.StreetJ. Murphy, 8 A. Naylor, 25 C. Nehrkorn, 23 H.N. Nelson, 23 F. Neves, 14 K.C. Oliver-Mallory, 9, 11 K.J. Palladino, 4 E.K. Pease, 9, 11 Q. Riffard, 9, 11 G.R.C. Rischbieter, 20 C. Rhyne, 18 P. Rossiter, 25 S. Shaw, 23, 21 T.A. Shutt, 1, 2, 3 C. Silva, 14 M. Solmaz, 23 V.N. Solovov, 14 P. Sorensen, 11 T.J. Sumner, 5 M. Szydagis, 20 D.J. Taylor, 16 W.C. Taylor, 18 B.P. Tennyson, 12 P.A. Terman, 26 D.R. Tiedt, 6 W.H. To, 27 M. Tripathi, 7 L. Tvrznikova, 9, 11, 12, * U. Utku, 21 S. Uvarov, 7 V. Velan, 9 R.C. Webb, 26 J.T. White, 26 T.J. Whitis, 1, 2, 3 M.S. Witherell, 11 F.L.H. Wolfs, 19 D. Woodward, 17 J. Xu, 10 K. Yazdani, 5 and C. Zhang 15 (LUX Collaboration) 1 Case Western Reserve University, Department of Physics, 10900 Euclid Avenue, Cleveland, Ohio 44106, USA 2 SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94205, USA 3 Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, 452 Lomita Mall, Stanford, California 94309, USA 4 University of Wisconsin-Madison, Department of Physics, 1150 University Avenue, Madison, Wisconsin 53706, USA 5 Imperial College London, High Energy Physics, Blackett Laboratory, London SW7 2BZ, United Kingdom 6 South Dakota School of Mines and Technology, 501 East St Joseph Street, Rapid City, South Dakota 57701, USA 7 University of California Davis, Department of Physics, One Shields Avenue, Davis, California 95616, USA 8 SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom 9 University of California Berkeley, Department of Physics, Berkeley, California 94720, USA 10 Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA 11 Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA 12 Yale University, Department of Physics, 217 Prospect Street, New Haven, CT 06511, USA 13 University of Liverpool, Department of Physics, Liverpool L69 7ZE, United Kingdom 14 LIP-Coimbra, Department of Physics, University of Coimbra, Rua Larga, 3004-516 Coimbra, Portugal 15 University of South Dakota, Department of Physics, 414E Clark Street, Vermillion, South Dakota 57069, USA 16 South Dakota Science and Technology Authority, Sanford Underground Research Facility, Lead, South Dakota 57754, USA 17 Pennsylvania State University, Department of Physics, 104 Davey Lab, University Park, Pennsylvania 16802-6300, USA 18 Brown University, Department of Physics, 182 Hope Street, Providence, Rhode Island 02912, USA 19 University of Rochester, Department of Physics and Astronomy, Rochester, New York 14627, USA 20 University at Albany, State University of New York, Department of Physics, 1400 Washington Avenue, Albany, New York 12222, USA 21 Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom 22 University of Maryland, Department of Physics, College Park, MD 20742, USA 23 University of California Santa Barbara, Department of Physics, Santa Barbara, California 93106, USA 24 University of Massachusetts, Amherst Center for Fundamental Interactions and Department of Physics, Amherst, Massachusetts 01003-9337 USA 25 University of Sheffield, Department of Physics and Astronomy, Sheffield, S3 7RH, United Kingdom 26 Texas A & M University, Department of Physics, College Station, Texas 77843, USA 27 California State University Stanislaus, Department of Physics, 1 University Circle, Turlock, California 95382, USA (Dated: March 21, 2019) The scattering of dark matter (DM) particles with sub-GeV masses off nuclei is difficult to detect using liquid xenon-based DM search instruments because the energy transfer during nuclear recoils is smaller than the typical detector threshold. However, the tree-level DM-nucleus scattering diagram can be accompanied by simultaneous emission of a Bremsstrahlung photon or a so-called “Migdal” arXiv:1811.11241v2 [astro-ph.CO] 20 Mar 2019

arXiv:1811.11241v2 [astro-ph.CO] 20 Mar 2019spiral.imperial.ac.uk/bitstream/10044/1/71579/2/1811... · 2019. 7. 19. · 14LIP-Coimbra, Department of Physics, University of Coimbra,

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  • Results of a Search for Sub-GeV Dark Matter Using 2013 LUX Data

    D.S. Akerib,1, 2, 3 S. Alsum,4 H.M. Araújo,5 X. Bai,6 J. Balajthy,7 P. Beltrame,8 E.P. Bernard,9 A. Bernstein,10

    T.P. Biesiadzinski,1, 2, 3 E.M. Boulton,9, 11, 12 B. Boxer,13 P. Brás,14 S. Burdin,13 D. Byram,15, 16

    M.C. Carmona-Benitez,17 C. Chan,18 J.E. Cutter,7 T.J.R. Davison,8 E. Druszkiewicz,19 S.R. Fallon,20 A. Fan,2, 3

    S. Fiorucci,11, 18 R.J. Gaitskell,18 J. Genovesi,20 C. Ghag,21 M.G.D. Gilchriese,11 C. Gwilliam,13 C.R. Hall,22

    S.J. Haselschwardt,23 S.A. Hertel,24, 11 D.P. Hogan,9 M. Horn,16, 9 D.Q. Huang,18 C.M. Ignarra,2, 3

    R.G. Jacobsen,9 O. Jahangir,21 W. Ji,1, 2, 3 K. Kamdin,9, 11 K. Kazkaz,10 D. Khaitan,19 R. Knoche,22

    E.V. Korolkova,25 S. Kravitz,11 V.A. Kudryavtsev,25 B.G. Lenardo,7, 10 K.T. Lesko,11 J. Liao,18 J. Lin,9

    A. Lindote,14 M.I. Lopes,14 A. Manalaysay,7 R.L. Mannino,26, 4 N. Marangou,5 M.F. Marzioni,8 D.N. McKinsey,9, 11

    D.-M. Mei,15 M. Moongweluwan,19 J.A. Morad,7 A.StreetJ. Murphy,8 A. Naylor,25 C. Nehrkorn,23 H.N. Nelson,23

    F. Neves,14 K.C. Oliver-Mallory,9, 11 K.J. Palladino,4 E.K. Pease,9, 11 Q. Riffard,9, 11 G.R.C. Rischbieter,20

    C. Rhyne,18 P. Rossiter,25 S. Shaw,23, 21 T.A. Shutt,1, 2, 3 C. Silva,14 M. Solmaz,23 V.N. Solovov,14 P. Sorensen,11

    T.J. Sumner,5 M. Szydagis,20 D.J. Taylor,16 W.C. Taylor,18 B.P. Tennyson,12 P.A. Terman,26 D.R. Tiedt,6

    W.H. To,27 M. Tripathi,7 L. Tvrznikova,9, 11, 12, ∗ U. Utku,21 S. Uvarov,7 V. Velan,9 R.C. Webb,26 J.T. White,26

    T.J. Whitis,1, 2, 3 M.S. Witherell,11 F.L.H. Wolfs,19 D. Woodward,17 J. Xu,10 K. Yazdani,5 and C. Zhang15

    (LUX Collaboration)1Case Western Reserve University, Department of Physics,

    10900 Euclid Avenue, Cleveland, Ohio 44106, USA2SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94205, USA

    3Kavli Institute for Particle Astrophysics and Cosmology,Stanford University, 452 Lomita Mall, Stanford, California 94309, USA

    4University of Wisconsin-Madison, Department of Physics,1150 University Avenue, Madison, Wisconsin 53706, USA

    5Imperial College London, High Energy Physics, Blackett Laboratory, London SW7 2BZ, United Kingdom6South Dakota School of Mines and Technology, 501 East St Joseph Street, Rapid City, South Dakota 57701, USA

    7University of California Davis, Department of Physics,One Shields Avenue, Davis, California 95616, USA

    8SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom9University of California Berkeley, Department of Physics, Berkeley, California 94720, USA

    10Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA11Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA12Yale University, Department of Physics, 217 Prospect Street, New Haven, CT 06511, USA

    13University of Liverpool, Department of Physics, Liverpool L69 7ZE, United Kingdom14LIP-Coimbra, Department of Physics, University of Coimbra, Rua Larga, 3004-516 Coimbra, Portugal

    15University of South Dakota, Department of Physics,414E Clark Street, Vermillion, South Dakota 57069, USA

    16South Dakota Science and Technology Authority,Sanford Underground Research Facility, Lead, South Dakota 57754, USA

    17Pennsylvania State University, Department of Physics,104 Davey Lab, University Park, Pennsylvania 16802-6300, USA

    18Brown University, Department of Physics, 182 Hope Street, Providence, Rhode Island 02912, USA19University of Rochester, Department of Physics and Astronomy, Rochester, New York 14627, USA

    20University at Albany, State University of New York, Department of Physics,1400 Washington Avenue, Albany, New York 12222, USA

    21Department of Physics and Astronomy, University College London,Gower Street, London WC1E 6BT, United Kingdom

    22University of Maryland, Department of Physics, College Park, MD 20742, USA23University of California Santa Barbara, Department of Physics, Santa Barbara, California 93106, USA

    24University of Massachusetts, Amherst Center for Fundamental Interactionsand Department of Physics, Amherst, Massachusetts 01003-9337 USA

    25University of Sheffield, Department of Physics and Astronomy, Sheffield, S3 7RH, United Kingdom26Texas A & M University, Department of Physics, College Station, Texas 77843, USA

    27California State University Stanislaus, Department of Physics,1 University Circle, Turlock, California 95382, USA

    (Dated: March 21, 2019)

    The scattering of dark matter (DM) particles with sub-GeV masses off nuclei is difficult to detectusing liquid xenon-based DM search instruments because the energy transfer during nuclear recoils issmaller than the typical detector threshold. However, the tree-level DM-nucleus scattering diagramcan be accompanied by simultaneous emission of a Bremsstrahlung photon or a so-called “Migdal”

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    electron. These provide an electron recoil component to the experimental signature at higher energiesthan the corresponding nuclear recoil. The presence of this signature allows liquid xenon detectorsto use both the scintillation and the ionization signals in the analysis where the nuclear recoil signalwould not be otherwise visible. We report constraints on spin-independent DM-nucleon scatteringfor DM particles with masses of 0.4-5 GeV/c2 using 1.4×104 kg·day of search exposure from the 2013data from the Large Underground Xenon (LUX) experiment for four different classes of mediators.This analysis extends the reach of liquid xenon-based DM search instruments to lower DM massesthan has been achieved previously.

    Introduction.—The two-phase xenon time projectionchamber (TPC) is the leading technology used to searchfor the weakly interacting massive particle (WIMP), afavored dark matter (DM) candidate, in the 5 GeV/c2

    to 10 TeV/c2 mass range. Despite substantial improve-ments in sensitivity over recent years, detecting DM re-mains an elusive goal [1–3]. Consistent progress in rulingout WIMP parameter space has resulted in a significantbroadening of efforts, including focusing on lighter parti-cles scattering off nuclei as possible DM candidates. Cur-rently, the intrinsic scintillation properties of nuclear re-coils prevent liquid xenon TPCs from reaching sub-GeVDM masses.

    Recently, Refs. [4, 5] proposed novel direct detectionchannels that extend the reach of liquid xenon detectorsto sub-GeV masses. They suggest that DM-nucleus scat-tering can be accompanied by a signal that results inan electron recoil (ER) at higher energy than the corre-sponding nuclear recoil (NR) in liquid xenon detectors.Since at low energies ERs produce a stronger signal thanNRs, this newly recognized channel enables liquid xenondetectors to reach sub-GeV DM masses. In the Large Un-derground Xenon (LUX) detector the 50% detection effi-ciency for NRs is at 3.3 keV [6], compared with 1.24 keVfor ERs [7].

    This Letter discusses searches of sub-GeV DM inthe LUX detector using two different mechanisms:Bremsstrahlung, first proposed in [4], and the Migdaleffect, reformulated in [5]. These atomic inelastic signalsare much stronger compared to the traditional elastic NRsignal for DM candidates with masses below ∼ 5 GeV/c2.

    Bremsstrahlung considers the emission of a photonfrom the recoiling atomic nucleus. In the atomic picture,the process can be viewed as the dipole emission of aphoton from a xenon atom polarized in the DM-nucleusscattering. The theoretical motivation and event ratesfor Bremsstrahlung have been derived in [4].

    For NRs in liquid xenon, it is usually assumed thatelectrons around the recoiling nucleus immediately fol-low the motion of the nucleus so that the atom remainsneutral. In reality, the electrons may lag resulting inionization and excitation of the atom [5]. When Migdaloriginally formulated the Migdal effect in 1941 [8], he as-sumed an impulsive force to describe this effect. How-ever, Ref. [5] reformulated the approach using atomicenergy eigenstates for their calculation, thus avoiding

    [email protected]

    the need to resolve the complex time evolution of thenucleus-electron system. Reference [5] contains the theo-retical motivation and presents the expected event ratesfor the Migdal effect. This analysis conservatively doesnot consider contributions from the xenon valence elec-trons (n = 5), since the surrounding atoms in the liquidmay influence the ionization spectrum from these elec-trons. Contributions from the n = 1, 2 electron shellsare negligible at DM masses considered in this study andwere also omitted. Furthermore, only electron energy in-jections caused by ionization were included in the signalmodel since excitation probabilities are much smaller.

    It should be emphasized that both NR and ER sig-nals are present when considering the Bremsstrahlungand Migdal effects. However, only the ER signal is usedin this analysis. The distance traveled by the photon orelectron will be less than the position resolution of thedetector, always resulting in a single S2. Higher interac-tion rates in the region of interest are expected from theMigdal effect.

    Both scalar and vector mediators are investigated. Thescalar mediator couples to Standard Model (SM) parti-cles by mixing with the SM Higgs boson, and thereforeits coupling is proportional to A2, where A is the atomicmass number. The vector mediator considered here, theso-called dark photon, couples to SM particles via mix-ing with the SM photon, so its coupling is proportionalto Z2 where Z is the charge number [9].

    Additionally, both heavy and light mediators werestudied, motivated by the many hidden (dark) sectorDM models [10, 11]. The DM form factor Fmed(ER)depends on the mass of the particle mediating the in-teraction at a given recoil energy. For a heavy media-tor with mmed � q, where q is the momentum trans-fer, Fmed can be approximated as 1. A heavy scalarmediator is typically assumed for the spin-independent(SI) elastic DM-nucleon cross section [12]. In the lightmediator limit, mmed � q and Fmed = q4ref/q4, wherethe SI DM-nucleon cross section is defined at a referencevalue q. For this analysis q = 1 MeV, a value typical formDM . 1 GeV/c2 [13]. Overall, this results in up to fourdifferent limits each for the Bremsstrahlung and Migdalsignals.

    Data analysis in LUX.—LUX is a dual-phase (liquid-gas) xenon TPC containing 250 kg of ultrapure liquidxenon in the active detector volume. Energy depositedby a particle interaction in the liquid induces two mea-surable signals: the prompt primary scintillation signalfrom VUV photons (S1), and ionization charge. An ap-

    mailto:[email protected]

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    plied electric field of 180 V/cm drifts these liberated elec-trons to the surface of the liquid, where the electrons areextracted into the gas and accelerated by a larger elec-tric field, producing secondary electroluminescence pho-tons (S2). Photons are detected by top and bottom ar-rays with 61 photomultiplier tubes (PMTs) each. ThePMT signals from both light pulses, S1 and S2, enablethe reconstruction of interaction vertices in three dimen-sions [14]. The ability to reconstruct positions of interac-tions in three dimensions allows fiducialization of the ac-tive volume. This avoids higher background regions nearthe detector walls and enables rejection of neutrons andγ-rays that scatter multiple times within the active detec-tor volume. Furthermore, the ratio of the S1 and S2 sig-nals is exploited to discriminate between ERs and NRs.Details regarding the construction and performance ofthe LUX detector can be found in [15].

    LUX collected data during two exposures in 2013 [6,16] and from 2014-16 [1]. The work presented here em-ploys WIMP search data with a total exposure of 95 livedays using 118 kg of liquid xenon in the fiducial volumecollected from April 24 to September 1, 2013, referredto as WS2013. These data have also been used to setlimits on spin-dependent interactions [17] and for axionand axionlike particle searches [18]. The performance ofthe detector during WS2013 is documented in [19]; onlyespecially relevant information is included here.

    Data presented here are identical to the final data setpresented in [6]. Only single scatter events (one S1 fol-lowed by one S2) are considered. The fiducial volume isdefined from 38-305 µs in drift time (48.6-8.5 cm abovethe faces of the bottom PMTs in z) and a radius < 20 cm.S1 pulses are required to have a two-PMT coincidenceand produce 1-50 detected photons (phd) [20]. The ital-icized quantities S1 and S2 indicate signal amplitudesthat have been corrected for geometrical effects and time-dependent xenon purity. Therefore, S1 can be below2.0 phd even when the twofold photon coincidence is sat-isfied, as discussed in [19]. A threshold of 165 phd rawS2 size is applied to mitigate random coincidence back-ground from small, isolated S2s.

    The total energy deposition E of ERs in the detector isdirectly proportional to the number of quanta produced:

    E = W (nγ + ne) = W

    (S1

    g1+S2

    g2

    ),

    where nγ is the number of photons and ne the initialnumber of electrons leaving the interaction site. Thedetector-specific gain factors g1 = 0.117 phd per photonand g2 = 12.2 phd per electron were obtained from cali-brations [19]. The efficiency for extracting electrons fromliquid to gas is 49%± 3%. The overall photon detectionefficiency for prompt scintillation, g1, is the product ofthe average light collection efficiency of the detector andthe average PMT quantum efficiency. The correspond-ing quantity for S2 light, g2, consists of the product ofthe electron extraction efficiency (from liquid to gas) andthe average single electron pulse size. The average energy

    needed to produce a single photon or electron W has avalue of (13.7± 0.2) eV/quanta [21].Electron recoil signal yields.—The response of the LUX

    detector to ERs was characterized using internal tritiumcalibrations performed in December 2013, directly fol-lowing WS2013. Tritiated methane was injected into thegas circulation to achieve a spatially uniform distributionof events dissolved in the detector’s active region, as de-scribed in [7]. This direct calibration is applied to buildthe signal model for this analysis. Figure 1 shows excel-lent agreement between the ER yields from the in situtritium calibrations and yields obtained from the NobleElement Simulation Technique (NEST) package v2.0 [22],used to model the ER response in the signal model. Thecomplementary behavior between the light and chargeyields is due to recombination effects described in [7, 23].Since this Letter considers recoils at the lowest energies,where recombination is small, it is limited by light pro-duction rather than charge yields.

    A 1.24 keV low-energy cutoff was applied in the signalmodel corresponding to 50% efficiency of ER detection(cf. Fig. 6 in [7]), which imposes a lower mass limiton DM sensitivity of 0.4 GeV/c2. The highest testedmass was chosen to be 5 GeV/c2 since at higher massesthe traditional elastic NR results in a larger event rateabove threshold than the Bremsstrahlung or Migdal ef-fects. The scattering rates for both the Bremsstrahlungand Migdal effects along with the traditional elastic NRsignal and the impact of the signal cutoff for several DMmasses are illustrated in Fig. 2.

    The expected event rate for a 1 GeV/c2 DM particlewith a cross section per nucleus of 1 × 10−35 cm2, thedetector ER efficiency, and the low-energy cutoff are il-

    FIG. 1. The light (blue) and charge (green) yields of tritiumER events as a function of recoil energy as measured in situby the LUX detector at 180 V/cm (solid lines) compared toNEST v2.0 simulations (dashed pink line). The bands in-dicate the 1-σ systematic uncertainties of the measurement.The dotted gray line shows the 1.24 keV energy thresholdimplemented in the analysis.

  • 4

    FIG. 2. Scattering rates in xenon for the Bremsstrahlung (solid blue) and Migdal effects (dashed teal). The DM-nucleusscattering rates resulting in elastic NR in LUX are also shown (dash-dot pink). Also shown is a signal cut off at 1.24 keV(dotted gray) applied in the analysis, corresponding to 50% efficiency of ER detection. Note that 50% efficiency for NR eventdetection occurs at 3.3 keV [6].

    lustrated in Fig. 3. The resulting signal model projectedon the two-dimensional space of S1-log10S2 with all anal-

    0.5 1.0 1.5 2.0 2.5 3.0 3.5Energy [keV]

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    FIG. 3. Illustration of the DM-nucleus scattering event ratefrom the Migdal effect with a heavy scalar mediator (solidblack line) for mDM = 1 GeV/c

    2 with a cross section pernucleus of 1 × 10−35 cm2. The scattering event rate was cal-culated following Ref. [5]. Also shown is the efficiency fromthe in situ tritium measurements performed by the LUX de-tector (dashed teal line). The hatched blue area indicates theevent rate considered for this analysis with tritium efficiencyand a 1.24 keV energy threshold (dotted gray line) applied.Data quality cuts are not included.

    ysis cuts applied is shown in Fig. 4.

    Background model.—An important distinction be-tween WS2013 and this Letter is that the sub-GeV signalfrom both the Bremsstrahlung and Migdal effects wouldresult in additional events within the ER classification,as identified by the ratio of S2 to S1 size. The standardWIMP search only has a small background from leakageof ER events into the NR band. However, both the sub-

    1

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    10-1

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    FIG. 4. The expected signal from DM-nucleus interactionsthrough the Migdal effect with a cross section per nucleusof 1 × 10−35 cm2 projected onto a two-dimensional space oflog10S2 vs. S1. Assumptions are the same as in Fig. 3 withadditional data quality cuts applied.

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    FIG. 5. Contours containing 95% of the expected DM sig-nal from the Bremsstrahlung and Migdal effects using NESTpackage v2.0 [22]. The solid amber contour indicates aBremsstrahlung signal of mDM = 0.4 GeV/c

    2 assuming aheavy scalar mediator (7.9 events). The other two con-tours are for the Migdal effect: The dashed teal contouris for mDM = 1 GeV/c

    2 assuming a heavy scalar media-tor (10.8 events), and the dash-dot light blue contour is formDM = 5 GeV/c

    2 assuming a light vector mediator (11.5events). The number in parentheses indicates the expectednumber of signal events within the contour for a given signalmodel with a cross section at the 90% C.L. upper limit. Thecontours are overlaid on 591 events observed in the regionof interest from the 2013 LUX exposure of 95 live days and145 kg fiducial mass (cf. Ref [6]). Points at radius < 18 cm areblack; those at 18-20 cm are gray since they are more likelyto be caused by radio contaminants near the detector walls.Distributions of uniform-in-energy electron recoils (blue) andan example signal from mDM =50 GeV/c

    2 (red) are indicatedby 50th (solid), 10th, and 90th (dashed) percentiles of S2 atgiven S1. Gray lines, with an ER scale of keVee at the top andLindhard-model NR scale of keVnr at the bottom, are con-tours of the linear-combined S1-and-S2 energy estimator [25].

    GeV signal and most backgrounds are in the ER band,so ER-NR discrimination cannot be used to reduce back-grounds in this analysis. The ER band is populated sig-nificantly, with contributions from γ-rays and β particlesfrom radioactive contamination within the xenon, detec-tor instrumentation, and external environmental sourcesas described in [24]. For further information about thebackground model, refer to [6, 19] as the backgroundmodel used in this Letter is identical.

    Results.— The sub-GeV DM signal hypotheses aretested with a two-sided profile likelihood ratio (PLR)statistic. For each DM mass, a scan over the SI DM-nucleon cross section is performed to construct a 90%confidence interval, with the test statistic distributionevaluated by Monte Carlo sampling using the RooSt-ats package [36]. Systematic uncertainties in backgroundrates are treated as nuisance parameters with Gaussianconstraints in the likelihood. Six nuisance parametersare included for low-z-origin γ-rays, other γ-rays, β par-

    FIG. 6. Upper limits on the SI DM-nucleon cross sec-tion at 90% C.L. as calculated using the Bremsstrahlungand Migdal effect signal models assuming a scalar media-tor (coupling proportional to A2). The 1- and 2-σ ranges ofbackground-only trials for this result are presented as greenand yellow bands, respectively, with the median limit shownas a black dashed line. The top figure presents the limitfor a light mediator with qref = 1 MeV. Also shown is alimit from PandaX-II [10] (pink), but note that Ref. [10]uses a slightly different definition of Fmed in their signalmodel. The bottom figure shows limits for a heavy media-tor along with limits from the SI analyses of LUX [1] (red),PandaX-II [2] (gray), XENON1T [26] (orange), XENON100S2-only [27] (pink), CDEX-10 [28] (purple), CDMSlite [29](teal), CRESST-II [30] (dark blue), CRESST-III [31] (lightblue), CRESST-surface [32] (cyan), DarkSide-50 [33] (green),NEWS-G [34] (brown), and XMASS [35] (lavender).

    ticles, 127Xe, 37Ar, and wall counts, as described in [6](cf. Table I). Systematic uncertainties from light yieldhave been studied but were not included in the final PLRstatistic since their effects were negligible. This is ex-pected as the error on light yield obtained from the tri-tium measurements ranges from 10% at low energies tosub 1% at higher energies. Moreover, slightly changingthe light yield is not expected to change the limit sig-nificantly since only a small fraction of events near the

  • 6

    applied energy threshold are affected.For an illustration of the expected location of the signal

    in the S1-log10S2 detector space, contours for variousDM masses with different mediators are overlaid on theobserved events from WS2013 shown in Fig. 5.

    Upper limits on cross section for DM masses from 0.4to 5 GeV/c2 for both the Bremsstrahlung and Migdaleffects assuming both a light and a heavy scalar medi-ator are shown in Fig. 6. Upper limits for a light anda heavy vector mediator for the Migdal effect were alsocalculated. The limits are scaled by Z2/A2 compared tothe scalar mediator case and can be found in [37]. Theobserved events are consistent with the expectation ofthe background-only hypothesis.

    Summary.—Contributions from the Bremsstrahlungand Migdal effects extend the reach of the LUX detec-tor to masses previously inaccessible via the standardNR detection method. The Bremsstrahlung photon andthe electron from the Migdal effect emitted from therecoiling atom boost the scattering signal for low massDM particles since the energy transfer is larger in theseatomic inelastic scattering channels than in the stan-dard elastic channel and the ER efficiency is significantlyhigher at low energies. This analysis places limits onSI DM-nucleon cross sections to DM from 0.4 GeV/c2

    to 5 GeV/c2 assuming both scalar and vector, and lightand heavy mediators. The resulting limits achieved usingthe Migdal effect, in particular, create results competi-tive with detectors dedicated to searches of light DM.Furthermore, this type of analysis will be useful to thenext-generation DM detectors, such as LZ [38] by extend-ing their reach to sub-GeV DM masses.

    Acknowledgments.—The authors would like to thankRouven Essig, Masahiro Ibe, Christopher McCabe, JosefPradler, and Kathryn Zurek for helpful conversations andcorrespondence. We would also like to thank the refereesfor their constructive comments and recommendations.

    This Letter was partially supported by theU.S. Department of Energy (DOE) under AwardNo. DE-AC02-05CH11231, DE-AC05-06OR23100,

    DE-AC52-07NA27344, DE-FG01-91ER40618, DE-FG02-08ER41549, DE-FG02-11ER41738, DE-FG02-91ER40674, DE-FG02-91ER40688, DE-FG02-95ER40917, DE-NA0000979, DE-SC0006605, DE-SC0010010, DE-SC0015535, and DE-SC0019066; theU.S. National Science Foundation under Grants No.PHY-0750671, PHY-0801536, PHY-1003660, PHY-1004661, PHY-1102470, PHY-1312561, PHY-1347449,PHY-1505868, and PHY-1636738; the Research Cor-poration Grant No. RA0350; the Center for Ultra-lowBackground Experiments in the Dakotas (CUBED);and the South Dakota School of Mines and Tech-nology (SDSMT). Laboratório de Instrumentaçãoe F́ısica Experimental de Part́ıculas (LIP)-Coimbraacknowledges funding from Fundação para a Ciênciae a Tecnologia (FCT) through the Project-GrantPTDC/FIS-NUC/1525/2014. Imperial College andBrown University thank the UK Royal Society fortravel funds under the International Exchange Scheme(IE120804). The UK groups acknowledge institutionalsupport from Imperial College London, UniversityCollege London and Edinburgh University, and fromthe Science & Technology Facilities Council forGrants ST/K502042/1 (AB), ST/K502406/1 (SS), andST/M503538/1 (KY). The University of Edinburgh is acharitable body, registered in Scotland, with Registra-tion No. SC005336.This research was conducted using computationalresources and services at the Center for Computationand Visualization, Brown University, and also the YaleScience Research Software Core.We gratefully acknowledge the logistical and technicalsupport and the access to laboratory infrastructure pro-vided to us by SURF and its personnel at Lead, SouthDakota. SURF was developed by the South DakotaScience and Technology Authority, with an importantphilanthropic donation from T. Denny Sanford. Itsoperation is funded through Fermi National AcceleratorLaboratory by the Department of Energy, Office of HighEnergy Physics.

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    Results of a Search for Sub-GeV Dark Matter Using 2013 LUX DataAbstract References